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New submitter Lee_Dailey sends this news from Quanta Magazine:
"Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality. 'This is completely new and very much simpler than anything that has been done before,' said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work. The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like "amplituhedron," which yields an equivalent one-term expression."

"They also claim to have found a "master amplituhedron" with infinitely many faces in infinitely many dimensions which should now be as important as the circle in two dimensions.;-) Its volume counts the "total amplitude" (?) of all processes; faces of this master jewel harbor the amplitudes for processes with finite collections of particles."

Also, computing proteins folding is probably going to get a serious performance boost too. If this proves to really work genetic engineering is going to enter a new phase.

Probably not.This just speeds up some mathematical methods used to calculate probability fields in quantum mechanical problems. So it will provide a certain linear speedup of those calculations (for example 1000 times faster).It will not however help with NP hard problems (like protein folding), because these would need real quantum computations (on a quantum computer) to reduce the exponential order of the problem into a lower order one.If a problem would take many times the age of the universe to calculate, then dividing that time by a small factor will not help much.

If a problem would take many times the age of the universe to calculate, then dividing that time by a small factor will not help much.

True enough. However, the fact that actual proteins manage to do it in a microsecond or less suggests there's a very easy way we just aren't aware of yet. Consider: it can be the case that the development of new mathematical tools works as a kind of Moore's Law for scientific research, making thing exponentially simpler with every step. This new mathematical tool by itself isn't much, but if the next improves the previous one by 1000 times, then next by another 1000 times, and so on and so forth, at some po

However, the fact that actual proteins manage to do it in a microsecond or less suggests there's a very easy way we just aren't aware of yet.

Nature doesn't calculate like we do, it works like a quantum computer. Meaning, all the possible outcomes of the calculation (a step in the shaping of the protein) occur at the same time (each has a certain probability of occurring). So basically nature "computes" every possibility in parallel and then picks an outcome at random, weighted by probability.

Consider: it can be the case that the development of new mathematical tools works as a kind of Moore's Law for scientific research, making thing exponentially simpler with every step.

This would basically mean that P=NP (a statement that is not yet proven nor disproven in mathematics). It's possible, but that would be a much, much bigger

So it will provide a certain linear speedup of those calculations (for example 1000 times faster).
It will not however help with NP hard problems (like protein folding), because these would need real quantum computations (on a quantum computer) to reduce the exponential order of the problem into a lower order one.

For any given (specific) NP hard problem, a 1000x speed increase in computation will result in a solution in 1/1000th of the time. It will still need to complete the same algorithmic steps, but it

The fact that nature (basically THE quantum computer) can fold a complex protein in a fraction of a second seems to demonstrate that at least some of these problems are solvable by QC in P time.Is this because the problem wasn't NP-hard to begin with (but it sure seemed that way)?Or don't we yet have the right QC algorithms to do this (it's a growing field)?Or maybe nature cheats and doesn't solve the same problem (but finds some local minimum in the energy landscape)?

A singularity nut. Your brain is a machine. It can be understood, decompiled, analyzed, improved and reimplemented. You're already an AI running on appropriate (and at some point in future becoming outdated) hardware.

But I'm hoping we never actually prove that souls exist. That's one door I'd prefer to remain closed. If science determined that souls exist, then we'd be figuring out ways to harness souls for energy. And then that'd bring up the whole question of what else is out there in that sphere of reality--and I'd really rather not draw a Nyarlathotep-analogue's attention.

No it isn't. Another example of an emergent property is the super fluidity of liquid helium. It is a property of a system that is not a property of its components nor immediately obvious from the properties of those components, but that arises when a large number of those parts interact as a system.

Just because you don't understand a word does not make it technobabble. Jargon yes, babble no.

I'm working on my PhD in math now and writing my thesis on complex systems. I'm going to call bullshit on that. While a lot of people throw the term around very loosely, emergence is a well-defined, known mathematical property of complex systems. I wouldn't go so far to say that we completely understand it on a biological level, but we can definitely study the properties of emergence through constructing a purely mathematical, complex system. But I'm not going to deny that our consciousness isn't emergent behavior, either. Neural networks are a textbook example of a complex system, and maybe the system for neural networks has emergence properties. I don't know, I can't claim to know, but it seems to fit with the math and science. To say emergence is technobabble nonsense is just ignorant, when it's a well defined property in a field of mathematics.

...kind of makes your original argument a bit moot, considering the proposed mathematical model really only applies to QM interactions

Not really. Consider: the best way to algorithmically test an airplane, if by best we mean the most accurate, would be to simulate every particle of it dealing with other particles. That's not the best in terms of speed though, so that we have useful simplifications in the form of the laws of aerodynamics. Those aren't as accurate as the former, but enough so. Similarly, once we really understand how cognition works (again, it doesn't necessarily require for us to go down into QM to find it out) we most pr

Lisi's E_8 conjecture [wikipedia.org] is somewhat more complicated than this one. For a start, the geometry of the E_8 group is richer than that of a mere amplituhedron. Others may note that Lisi's conjecture also includes gravitation in its unification, while TFA appears to be only about particle families.

Unified theories are more attractive, but every new way of looking at physics (that accurately models reality) is one more potential avenue of insight into the fundamental nature of our universe. This is definitely an exciting discovery, though I do not share their enthusiasm for boiling all of reality down to particle interactions with geometry, rather than statistics.

The Copenhagen interpretation of QM is a disgrace, and any self-respecting scientist should be ashamed to support a theory that hides reali

This isn't a particle so much as methodology; physicists have discovered that certain particles fit together in a certain way. Apparently before this it was a huge clusterfuck. Its like the mandelbrot set; its not a physical "thing", but its damn useful. To physicists only, I think, but we'll see.

The important bit here is why? Why does this methodology work so well. Is it because that deep down on a very fundamental level this "Geometry" is hard coded in the way the universe works? If so. What does this tell us about how things really work?

The important bit here is why? Why does this methodology work so well. Is it because that deep down on a very fundamental level this "Geometry" is hard coded in the way the universe works? If so. What does this tell us about how things really work?

That's a pretty good question. I've been wondering about that too, given the convergence between our definitions of entropy and Kolmogorov complexity, which describes how much information is encoded in a signal (also tied in with Shannon's law). It hits directly into the heart of the question: what is information and how does it relate to reality? At a basic level, our universe may be comprised of "information", or rather: a signal on top of noise.

This new discovery seems to suggest that at the most basic level, particles can be described as a mathematical function on top of some sort of "white noise" as well. I wonder how long it will take to converge the two ideas. If ever.

In any case, exciting times are ahead for so-called computer scientists that deal with things like geometric algorithms. I predict a hot demand for top mathematicians in that field to arise very soon.

Anyway, exciting times to be a theoretical physicist! Everyone expecting breakthroughs coming from the LHC and the experimental boys and girls, and now suddenly, out of left field the theoretical physicists come back with a big right hook out of nowhere:)

Guys, we've been down this road about a million times in physics. Just because a mathematical model simplifies certain calculations, does not mean that the actual underlying physical geometry matches the theoretical model. Mathematicians have been adding extra dimensions to equations and finding they simplify things for years. It doesn't mean we live in a 27 dimension manifold. All direct observations to date point to a 3D universe.

Ummm... hang on a second. Won't any direct observation we make as 3D critters point to a 3D universe? Isn't that sort of inherent to us being only able to perceive 3D?

I'm not sure how we'd do any direct observations in any other dimensions. (Honestly, not a flame, I'm genuinely puzzled by how we could see anything else and every now and then something like this hurts my head)

I'm not sure how we'd do any direct observations in any other dimensions. (Honestly, not a flame, I'm genuinely puzzled by how we could see anything else and every now and then something like this hurts my head)

First, we assume a spherical cow, now that we have a more efficient source of steak and cheese, we get to the real work. The real work involves creating an infinitely large perfectly flat mirror. Since we don't know of any way to push or pull something into dimensions that we cannot directly observe, we anchor the infinite mirror to the earth (or a designated extraplanetary observatory) and wait. The odds that a 14-dimensional object/creature/other would not accidentally bump into an infinite functionally 2 dimensional surface approach zero as your timescale expands. Therefore, we just wait until the mirror rotates in a way we cannot intuitively describe and effectively ceases to exist in our 3 dimensional space (or drags the earth with it into some other 3 dimensional subset of realities).

Unless some of the dimensions are curved, then you need a hypercubic pig.

This is basically what particle colliders do. Imagine that We lived in a 2D universe like a sheet of paper. The particle collider smashes atoms and we observe the splash it makes. From the splashes around the collision, we see that things seem to have appeared out of nowhere, but if We assume that there is actually a 3rd dimension, we can perceive that the particles/energy didnt just appear, but traveled on an unseen dimension. That is what a particle collider does, if You can wrap Your head around it,

From the splashes around the collision, we see that things seem to have appeared out of nowhere, but if We assume that there is actually a 3rd dimension, we can perceive that the particles/energy didnt just appear, but traveled on an unseen dimension. That is what a particle collider does, if You can wrap Your head around it, but in our 4D length/width/height/moment range of observation.

You could take the more rational approach and believe that we simply lack the technology to detect and measure what really happened. Naw, you would rather claim that the particle visited an invisible magical world! Was it Charon pulling the particle across the river Styx for a visit perhaps?

You could take the more rational approach and believe that we simply lack the technology to detect and measure what really happened. Naw, you would rather claim that the particle visited an invisible magical world!

I'm not saying he's necessarily right, but if a particle moves along an unseen dimension, its movements are likely still predictable if you've got the mathematical chops. If you're at a point where you can accurately predict something, that's what I'd call a good start.

But hey if you'd rather just throw your hands in the air and say fuck it I don't know, go for it.

You know how neutrinos have this tendency to change flavors as they pass through time (i.e. neutrino oscillation)? One nifty way of viewing it is that they're 4D objects simply with a spin in the fourth dimension. If you're into the physics, you'll note the same sort of calculations are used in the Pontecorvo–Maki–Nakagawa–Sakata matrix as are used by game engines when calculating the 2D representations of 3D virtual objects: You just then need to do basic matrix transformations to derive the result.

Check out Richard Feynman's lecture regarding space-time and his analogy of bugs on a sphere. If you tell them that the rule for making a square is to go N units in one direction, then turn 90 degrees and repeat until you complete the square, they would find that they cannot actually make a square. This leads them to conclude that there is "something wrong" with their space.

The point is that while the underlying nature of their universe as a sphere is unavailable to them because they cannot escape it to see the bigger picture, they can still infer that because Euclid's rules of geometry don't work there must be something going on that they can't see. Moreover, they should be able to guess that there is curvature - without knowing for sure - because of exactly how the rules break down.

This is essentially what people talk about when they refer to the difference between larger objects like clumps of atoms and smaller ones like electrons and quarks. For some reason our 3D (technically it's 4D according to Einstein) universe only behaves "normally" until we start measuring it at a small scale. Then we start seeing where our rules about the behavior of "observable" objects - i.e., the stuff we can perceive with our senses - break down and are replaced by the true nature of the subatomic universe. In other words, when we look at quarks do stuff, we can no longer make the square.

Constructs like the one described above are the result of us trying to get our little bug heads around the way in which our every day rules break down when really tiny things are involved. It's a way for the bugs to correct Euclid to account for the spherical nature of things.

Considering that we have evolved all these different sensory organs to help us survive, I'm sure that if perceiving a 4th dimension granted any biological advantage at all, we would be able to perceive it. Sorry to be anthropic about it but my field is biology not physics, lol.

Just because a mathematical model simplifies certain calculations, does not mean that the actual underlying physical geometry matches the theoretical model.

That's not really a problem if all you want to do is simplify the mathematics. Besides which, that was pretty much the reason that early astronomers weren't branded as heretics; they just said that a heliocentric model made the calculations easier, and that they weren't suggesting that they reflected reality (although they did).

All direct observations to date point to a 3D universe.

Well no shit Sherlock. It's rather hard to observe dimensions that your eyes can't see and your mind can't design instruments to detect. Oh... and, you know, time?

and that they weren't suggesting that they reflected reality (although they did).

What's interesting there is we say it reflects reality because it makes the calculations easier. Other than the math and mental models being easier to grasp, there really is no good reason to say the earth goes around the sun* rather than the sun going around the Earth. We just all decided that the calculations being easier trumps the very intuitive model that the sun circles the Earth. You can construct a perfectly rational model of the Universe from the non-inertial frame of reference that holds the Earth as stationary. It's just full of epicycles etc..

It's a fairly rare achievement for mass society to replace the naively simpler model of the stationary Earth.

*for the sake of argument, lets not get into them both orbiting a common barycentre; the argument extends to that as well anyway.

What's interesting there is we say it reflects reality because it makes the calculations easier.

That really is the most interesting thing in this discussion. Essentially we are making a leap of faith, that simpler models are more likely to be true as long as they continue to support the data and allow us to make predictions. But it is at root an aesthetic judgement: beauty is truth, and truth is beautiful. It is the essence of rationality.

It's cool to see how Feynman's diagrams may be like the epicycles of the earth-centered view of the universe: they can be made to work as long as you keep refin

It seems like their math is like good code. You can get a program to do the same thing in 10 lines what someone else tried to do in 1,000 lines. They're both describing the same basic function, but one is doing it via a brute force in a roundabout way and the other is doing it much more directly.

Then again, mathematicians tend to be a bit crazy. I remember reading one bio-mathematics person determining that bees do their little waggle dances in nine dimensions projected onto two, and I thought she was insane.

Mathematicians have been adding extra dimensions to equations and finding they simplify things for years. It doesn't mean we live in a 27 dimension manifold. All direct observations to date point to a 3D universe.

What observations would those be? If assuming 27 dimensions gets the same results as assuming 3 dimensions, then you can't tell which one the universe is through observation. And if 27 dimensions is a simpler model, then Occam's razor suggests we should indeed consider our home to be a 27D manifol

IANAPOM (I am not a physicist or mathematician), but from what I could gather from the article, it sounds like this isn't a new model that approximates the old, more complicated one, but rather a massive simplification of the existing one that produces provably identical results in all cases. To drastically oversimplify using my extremely limited understanding while putting it in terms I can wrap my brain around, it sounds like when you first learn about the arithmetic series in calculus (e.g. the summation of i from 0 to n). At first, the only way you can approach it is by actually adding 0 + 1 +... + (n-1) + n, but eventually you learn that you can skip that whole process if i starts at 0 and use n*(n+1)/2 to reach the result with far less work, and then you're shown how to derive that formula yourself.

It sounds like something similar here. They previously had to calculate the results of every single Feynman diagram and then sum them together to reach a final result, which would involve billions upon billions of calculations for even a very simple particle interaction. Now, however, rather than having to calculate all of the component parts and summing them, they've derived a formula that produces the same answers with far less work.

Again, I may be way off, but that's the takeaway I had from the article.

Feynman diagrams are based on the idea that there is framework of time and space, more specifically basically the same time and space that we perceive in everyday life.

This new model apparently takes a simpler view of the problem by not caring about time and space. I suppose you could say that time and space could be viewed as emergent properties of this geometric object that they have come up with / discovered.

I have to say, I'm disappointed whenever the "better analogy" isn't a car one. So, here's my attempt at one!

It's like saying that we currently build cars by manufacturing the individual pieces and then assembling them, but this sort of thing is like making Star Trek replicator that can spit out cars all willy-nilly. It'd produce the same result, but with a fraction of the steps that it used to take and a lot less cruft like "time" and "space" (and "jobs").

My impression after reading the article is that this allows for easier predictions of the outcomes of particle interactions, like you might show with Feynman diagrams [wikipedia.org] (particle decay, collisions that produce different particles, etc). Basically, the kinds of things that we'd study in a particle accelerator (so, quantum interactions, rather than classical ones).

does the simplification that it mentions, mean that simulations will be way faster? does it in any way affect the n-body problem simulations ?

An awesome question. And, basically, an awesome idea. I would think that if you can set up a numeric experiment that virtually represents fundamental particles and their interactions, and you already know more or less the trajectories in some n-dimensional space (through this new discovery), then you can probably greatly optimize your algorithms since you will a priori know whereabouts to look for solutions: you would not need to sweep everything.

Well, if this concept pans out, we'd be able to calculate all kinds of particle interactions we'd never be able to observe otherwise because those interaction would just be different facets of The One True Gem. Who knows what kind of amazing things we'd find a facet or two over from our current understanding?

Well, if this concept pans out, we'd be able to calculate all kinds of particle interactions we'd never be able to observe otherwise because those interaction would just be different facets of The One True Gem

Given how many insane conspiracy theories are lately turning out to be not completely insane, I'm just waiting for Congress to rip off their masks and reveal their true identities: Lizard Men from the Hollow Earth.

Since the N=4 supersymmetric Yang-Mills theory is a toy theory that does not describe the real world, the relevance of this theory to the real world is currently unknown, but it provides promising directions for research into theories about the real world.

If one assumes that Special Relativity and Quantum Mechanics are correct, and there is no observational evidence that they are not, then Yang-Mills theory, or something very much like it, is inevitable. It arises from the need for conservation of the various charges each force.

If one assumes that Special Relativity and Quantum Mechanics are correct, and there is no observational evidence that they are not, then Yang-Mills theory, or something very much like it, is inevitable. It arises from the need for conservation of the various charges each force.

xkcd's Purity [xkcd.com]. In the other hand, can't take out of my head that Kepler [wikipedia.org] originally tried to match that the orbits of the 6 known planets at that time with the shapes of the platonic solids, and this could face the same risk.

I know some of you are thinking this, but it's not, ok.
It's not some complicated mess of geometrical shapes to describe the universe in kaleidoscopic glory as envisioned by a lunatic with a Spirograph.

Just as alchemy eventually led to chemistry the mystics win again. The logic in theology is that God by definition would be the ultimate craftsman. That means no errors and no waste and no undue use of effort or energy. So just how God make a creation? Obviously endless universes could be set in motion by a science that resembles computer programs. Yes, humanity is nothing but the gorilla with a sledge hammer playing whack-a-mole on a monitor.

One of the things the article says is that space and time may not be fundamental properties of nature, but properties that emerge (i.e., are the result of) a more fundamental reality.

Warning: IANAP. But with some axioms, it is possible to reach the same conclusion.

Imagine a simple experiment with an electron source and a detector. An electron is emitted in the direction of a detector. The experiment is set up such that while travelling towards the detector, the electron does not interact. More precisely, in between the emitter and the detector, the electron does not exchange any energy. Then, the electron hits the detector and becomes detected (interaction two).

Has the electron physically travelled in the space between the electron source and the detector? May it be assumed that in between the interaction with the emitter and its subsequent interaction with the detector the electron is physically present?

Obviously, it is impossible to establish that the electron is present between the emitter and the detector without actually interacting with the electron. It is therefore herewith observed that any assumptions about physical presence of the electron in between the source and the detector can not be experimentally verified. More generally, it is observed that the assumption of physical presence of any elementary particle in between two interactions can not be falsified.

Equally impossible to falsify is the assumption that in between the emitter and the detector, the electron in the experiment was not physically present. This assumption implies that (in the reference frame of the observer) the electron disappeared at the emitter and reappeared at the detector, and did not take up any physical space at any time in between. In between interactions, the representation of the electron disappeared and became unobservable. For as far as an observer can tell, the electron disappeared from the universe completely in between interactions.

Since obviously, properties about the electron are preserved in between interactions, the electron must still somehow being represented – i.e., the representation of the electron has clearly not disappeared from the universe.

The notion “observable universe” is therefore being introduced to make the distinction between interactions which can be observed, and the herewith theorized part of the universe that is apparently capable of at least holding a representation of an elementary particle and which can not be observed.

Observable universe: The part of the universe in which an interaction manifests itself.

Let us formulate the following two axioms:

Axiom 1: An interaction is instantaneous, i.e., it lasts for an infinitely small amount of time.Axiom 2: An elementary particle only exists in the observable universe at the moment of its interaction.

Notice that axiom 1 and 2 are unfalsifiable. Consider the reverse of axiom 2:

Reverse of Axiom 2: An elementary particle physically exists in the observable universe in the time that passes (in the reference frame of an observer) between two interactions.

This axiom is equally unfalsifiable, since physical presence of an elementary particle can only be proven by interacting with it. The reverse of axiom 1, which would postulate that an interaction lasts a non-zero amount of time, is equally unfalsifiable.

Elementary particles have no internal structure and are considered point particles. In other words, an elementary particle does not take up any physical space. If we assume that everything in the observable universe consists of elementary particles, then it follows that all particles that exist in the universe do not take up any space. The aggregate volume of all elementary particles is zero.

Combined, axioms 1 and 2 state that in between two interactions, an elementary particle is not present in the observable universe. A particle only manifests itse

The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity.

...And unitarity holds that the probabilities of all possible outcomes of a quantum mechanical interaction must add up to one.

I'm probably being very naive attempting to understand this article that has probably already been massively dumbed down, but, how can the probabilities of all possible outcomes of an interaction not add up to one? Surely they add up to one by definition, otherwise they are not probabilities? For example outcome X having a probability of 1/3 means, on average, you can multiply the number of times you observe the interaction by 1/3 and get the expected number of times you would see outcome X. If the probabilities in your statistical trials didn't add up to 1, doesn't that mean adding up the numbers of individual outcomes observed would give a number bigger (or smaller) than the total number of interactions observed? Obviously it cannot mean that, as that fails basic arithmetic.

I can imagine tossing a fair coin - heads has probability 0.5, tails 0.5, total 1. So now how about a 3 sided coin without unitarity? Let's say the probability of heads is still 0.5, tails 0.5 but it has a third side, bodies that also has probability 0.5 of occurring. That sounds mathematically impossible. It could be a mind-reading coin, where you pick heads and find that then occurs on half your coin tosses. Later you pick tails, and that occurs on half your coin tosses, but when you pick bodies, that also occurs on half of those coin tosses. OK, I give up! Can anyone who really understands unitarity enlighten me please? Is this anything like the uncertainty principle?

oh really? then why don't you - who obviously are not as deluded as the rest of the scientists - enlighten them and us about your centuries forward way of thinking by actually putting your claims to work ?

What do you mean with "centuries forward"?Your parent correctly pointed out that we have centuries (and millenia) OLD knowledge, which most modern scientist lack.And he dis not claim anything... he only pointed out facts.

I think that etash is right, though. Just because this new viewpoint ("Point of view is worth 80 IQ points", as Alan Kay says) is "geometric" doesn't automatically mean that it's the same "geometry" that was practiced by Ancient Greeks. Just as what we mean by "algebra" today is only superficially related to what the Arabs called "algebra" - or what the Babylonians didn't call algebra but were doing anyway.

What's ironic about your post is you've only stuck to western science, neglecting to point out how those things were known even millenia before the greeks. Don't be too harsh on people ignorant of history, we all, like you have demonstrated, have blind spots.

It looks like Wolfram was onto something in A New Kind of Science with his approach to replacing complex equations with simple rules.

I'd say Plato (perhaps Pythagoras) was onto something when he basically said that math is the fundamental everything of everything. Yep, the guy was wrong on the details, but what damn fine intuitions he managed to have 2400 years ago. No matter what we do we always end up referring back to him...

It looks like Wolfram was onto something in A New Kind of Science with his approach to replacing complex equations with simple rules.

I'd say Plato (perhaps Pythagoras) was onto something when he basically said that math is the fundamental everything of everything. Yep, the guy was wrong on the details, but what damn fine intuitions he managed to have 2400 years ago. No matter what we do we always end up referring back to him...

And perhaps Zeno and the Eleatics who maintained that "Space and time can be neither continuous nor discrete. What could they possibly be if neither continuous nor discrete, these are the only options we can conceive of. Therefore space and time must be completely different to how we conceive of them and, perhaps, don't exist at all." (this was the purpose of the 'Zenos paradoxes'.